College Algebra & Trigonometry, 2018a

8.2. THE TRIGONOMETRIC RATIOS 351
8.2 The Trigonometric Ratios
There are six common trigonometric ratios that relate the sides of a right triangle
to the angles within the triangle. The three standard ratios are the sine, cosine and
tangent. These are often abbreviated sin, cos and tan. The other three (cosecant,
secant and cotangent) are the reciprocals of the sine, cosine and tangent and are
often abbreviated csc, sec, and cot.
θ
hypotenuse
adjacent
opposite
Given an angle situated in a right triangle, the sine function is defined as the ratio
of the side opposite the angle to the hypotenuse, the cosine is defined as the ratio
of the side adjacent to the angle to the hypotenuse and the tangent is defined as
the ratio of the side opposite the angle to the side adjacent to the angle.
sin θ = opp
hyp
cos θ = adj
hyp
tan θ = opp
adj
A common mneumonic device to help remember these relationships is
–SOHCAHTOA– which identifies the Sin as Opp over Hyp Cos as Adj over Hyp
and the Tan as Opp over Adj.